365-3/8x=x+2

Solution for 365-3/8x=x+2 equation:

365-3/8x=x+2

We move all terms to the left:

365-3/8x-(x+2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

-3/8x-x-2+365=0

We multiply all the terms by the denominator


-x*8x-2*8x+365*8x-3=0

Wy multiply elements

-8x^2-16x+2920x-3=0

We add all the numbers together, and all the variables

-8x^2+2904x-3=0

a = -8; b = 2904; c = -3;
Δ = b2-4ac
Δ = 29042-4·(-8)·(-3)
Δ = 8433120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8433120}=\sqrt{16*527070}=\sqrt{16}*\sqrt{527070}=4\sqrt{527070}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2904)-4\sqrt{527070}}{2*-8}=\frac{-2904-4\sqrt{527070}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2904)+4\sqrt{527070}}{2*-8}=\frac{-2904+4\sqrt{527070}}{-16}
$